Theorems · Theorem · group theory
AddSubmonoid.list_sum_mem
∀ {M : Type u_1} [inst : AddMonoid M] (s : AddSubmonoid M) {l : List M}, (∀ x ∈ l, x ∈ s) → l.sum ∈ sSum of a list of elements in an AddSubmonoid is in the AddSubmonoid.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- list_sum_memproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.multiset_noncommSum_memproof · cited by 2
- convex_list_sumproof · cited by 0